Undergraduate Topology: A Working Textbook

Paperback | August 24, 2014

byAisling McCluskey, Brian McMaster

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This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors'combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp ideas precisely and to argue with straight and careful logic. Research and long experience in undergraduate mathematics education suggests that an optimal way to learn such asubject is to teach it to yourself, pro-actively, by guided reading of brief skeleton notes and by doing your own spadework to fill in the details and to flesh out the examples. This text will facilitate such an approach for those learners who opt to do it this way and for those instructors whowould like to encourage this so-called "Moore approach", even for a modest segment of the teaching term or for part of the class. In reality, most students simply do not have the combination of time, background and motivation needed to implement such a plan fully. The accessibility, flexibility and completeness of this text enable it to be used equally effectively for more conventional instructor-led courses. Critically, itfurnishes a rich variety of exercises and examples, many of which have specimen solutions, through which to gain in confidence and competence.

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This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors'combined university teaching experience stimu...

Aisling McCluskey graduated at Queen's University Belfast with a doctorate in Pure Mathematics (topology) in 1990 and subsequently was awarded a postdoctoral fellowship in Toronto in 1991. She was appointed to a permanent lectureship in Mathematics in the National University of Ireland (NUI), Galway, Ireland in January 1992. Since then...
Format:PaperbackDimensions:160 pagesPublished:August 24, 2014Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198702345

ISBN - 13:9780198702344

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Table of Contents

Preface1. Introduction2. Topological Spaces3. Continuity and Convergence4. Invariants5. Base and Product6. Separation AxiomsEssential ExercisesSolutions to Selected ExercisesFurther Reading

Editorial Reviews

"This is a well-motivated guided tour through the main areas of modern general topology. Because of this, I highly recommend it both as a textbook for advanced undergraduates and as a main resource for anyone setting out to learn the subject on their own." --Paul Bankston, Marquette University